Three-dimensional transient heat conduction analysis by boundary knot method

Abstract

This paper makes the first attempt to apply the boundary knot method (BKM), in conjunction with dual reciprocity technique, for the solution of three-dimensional transient heat conduction problems. The BKM is a meshless, integration-free, easy-to-program boundary-only numerical technique for high-dimensional problems. The first step of our strategy is to use the finite difference method for temporal derivative to convert the transient heat conduction equation into a nonhomogeneous modified Helmholtz equation. And then the corresponding nonhomogeneous problem is solved using the proposed BKM strategy in conjunction with dual reciprocity technique. Four benchmark numerical examples are investigated in detail, and the numerical results show that the present scheme has the merits of high accuracy, wide applicability, good stability, and rapid convergence and is appealing to solve 3D transient heat conduction problems.